, Volume 48, Issue 3, pp 279–289 | Cite as

Electrophysiological markers of newly acquired symbolic numerical representations: the role of magnitude and ordinal information

  • Rebecca Merkley
  • Andria Shimi
  • Gaia Scerif
Original Article


It is not yet understood how children acquire the meaning of numerical symbols and most existing research has focused on the role of approximate non-symbolic representations of number in this process (see Piazza, (Trends in Cognitive 14(12):542–551, 2010). However, numerical symbols necessitate an understanding of both order and magnitude, therefore order likely also plays a role in learning about number. Here, we used an artificial symbol-learning paradigm to contrast learning approximate numerical magnitude with learning numerical order. Thirty-two adult participants were randomly assigned to either the magnitude training group, in which they were trained to associate novel abstract symbols with non-symbolic numerical magnitudes, or the order training group, in which they were taught the ordinal sequence of the symbols, in analogy to the count sequence. Subsequently, electroencephalographic (EEG) data were recorded while participants completed a magnitude comparison task with the newly learned symbols. Comparing these newly acquired symbols affected event related potentials (ERPs) in a way that resembled comparisons of real numerical symbols [e.g. Temple & Posner, (Proc Natl Acad Sci USA 95(13):7836–7841, 1998)]. Furthermore, these ERP effects did not differ across learning groups, suggesting that adults formed similar representations regardless of method of instruction. In turn, the current findings highlight the potential role of ordinal information in symbolic acquisition.


Order Magnitude ERPs Symbol 



R. M. is supported by the Natural Sciences and Engineering Research Council, Canada (NSERC) and A. S. and G. S. are supported by a James S. McDonnell Foundation Understanding Human Cognition Award.


  1. Carey, S. (2009). The Origin of Concepts. New York: Oxford University Press.CrossRefGoogle Scholar
  2. De Smedt, B., Noël, M.-P., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends in Neuroscience and Education, 1–8. doi: 10.1016/j.tine.2013.06.001.
  3. Dehaene, S. (1996). The organization of brain activations in number comparison: event-related potentials and the additive-factors method. Journal of Cognitive Neuroscience, 8(1), 47–68. doi: 10.1162/jocn.1996.8.1.47.CrossRefGoogle Scholar
  4. Dehaene, S. (2011). The number sense: how the mind creates mathematics, revised and updated edition. New York: Oxford University Press.Google Scholar
  5. Gebuis, T., & Reynvoet, B. (2012). The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General, 141(4), 642–648. doi: 10.1037/a0026218.CrossRefGoogle Scholar
  6. Göbel, S. M., Watson, S. E., Lervåg, A., & Hulme, C. (2014). Children’s arithmetic development: it is number knowledge, not the approximate number sense, that counts. Psychological Science, 25(3), 789–798. doi: 10.1177/0956797613516471.CrossRefGoogle Scholar
  7. Hyde, D. C., & Spelke, E. S. (2009). All numbers are not equal: an electrophysiological investigation of small and large number representations. Journal of Cognitive Neuroscience, 21(6), 1039–1053.CrossRefGoogle Scholar
  8. Leibovich, T., & Ansari, D. (in press). The symbol-grounding problem in numerical cognition: a review of theory, evidence and outstanding questions. Canadian Journal of Experimental Psychology.Google Scholar
  9. Libertus, M. E., Woldorff, M. G., & Brannon, E. M. (2007). Electrophysiological evidence for notation independence in numerical processing. Behavioral and Brain Functions : BBF, 3, 1. doi: 10.1186/1744-9081-3-1.CrossRefGoogle Scholar
  10. Lyons, I. M., & Ansari, D. (2009). The cerebral basis of mapping nonsymbolic numerical quantities onto abstract symbols: an fMRI training study. Journal of Cognitive Neuroscience, 21(9), 1720–1735. doi: 10.1162/jocn.2009.21124.CrossRefGoogle Scholar
  11. Lyons, I. M., Ansari, D., & Beilock, S. L. (2012). Symbolic estrangement: evidence against a strong association between numerical symbols and the quantities they represent. Journal of Experimental Psychology. General. doi: 10.1037/a0027248.
  12. Lyons, I. M., & Beilock, S. L. (2009). Beyond quantity: individual differences in working memory and the ordinal understanding of numerical symbols. Cognition, 113(2), 189–204. doi: 10.1016/j.cognition.2009.08.003.CrossRefGoogle Scholar
  13. Lyons, I. M., & Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121(2), 256–261. doi: 10.1016/j.cognition.2011.07.009.CrossRefGoogle Scholar
  14. Lyons, I. M., Nuerk, H. C., & Ansari, D. (2015). Rethinking the implications of numerical ratio effects for understanding the development of representational precision and numerical processing across formats. Journal of Experimental Psychology: General, 144(5), 1021.CrossRefGoogle Scholar
  15. Merkley, R. (2015). Beyond number sense: Contributions of domain-general processes to the development of numeracy in early childhood. Unpublished doctoral thesis. University of Oxford.Google Scholar
  16. Merkley, R., & Scerif, G. (2015). Continuous visual properties of number influence the formation of novel symbolic representations. The Quarterly Journal of Experimental Psychology68(9), 1860-1870. doi: 10.1080/17470218.2014.994538.CrossRefGoogle Scholar
  17. Miller, G. A. (1956). The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological review, 63(2), 81.CrossRefGoogle Scholar
  18. Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215(5109), 1519.CrossRefGoogle Scholar
  19. Piazza, M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences, 14(12), 542–551. doi: 10.1016/j.tics.2010.09.008.CrossRefGoogle Scholar
  20. Price, G. R., Palmer, D., Battista, C., & Ansari, D. (2012). Nonsymbolic numerical magnitude comparison: reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults. Acta Psychologica, 140(1), 50–57. doi: 10.1016/j.actpsy.2012.02.008.CrossRefGoogle Scholar
  21. Prinzmetal, W., McCool, C., & Park, S. (2005). Attention: Reaction time and accuracy reveal different mechanisms. Journal of Experimental Psychology: General, 134, 73–92.CrossRefGoogle Scholar
  22. Sasanguie, D., Defever, E., Maertens, B., & Reynvoet, B. (2013). The approximate number system is not predictive for symbolic number processing in kindergartners. The Quarterly Journal of Experimental Psychology, 67, 271–280. doi: 10.1080/17470218.2013.803581.CrossRefGoogle Scholar
  23. Szűcs, D., & Csépe, V. (2004). Similarities and differences in the coding of numerical and alphabetical order using acoustic stimulation as revealed by event-related potentials in humans. Neuroscience Letters, 360(1–2), 65–68. doi: 10.1016/j.neulet.2004.02.038.CrossRefGoogle Scholar
  24. Temple, E., & Posner, M. I. (1998). Brain mechanisms of quantity are similar in 5-year-old children and adults. Proceedings of the National Academy of Sciences of the United States of America, 95(13), 7836–41. Retrieved from
  25. Turconi, E., Campbell, J. I. D., & Seron, X. (2006). Numerical order and quantity processing in number comparison. Cognition, 98(3), 273–285. doi: 10.1016/j.cognition.2004.12.002.CrossRefGoogle Scholar
  26. Turconi, E., Jemel, B., Rossion, B., & Seron, X. (2004). Electrophysiological evidence for differential processing of numerical quantity and order in humans. Brain Research. Cognitive Brain Research, 21(1), 22–38. doi: 10.1016/j.cogbrainres.2004.05.003.CrossRefGoogle Scholar
  27. Tzelgov, J., Yehene, V., Kotler, L., & Alon, A. (2000). Automatic comparisons of artificial digits never compared: learning linear ordering relations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26(1), 103.Google Scholar
  28. Van Opstal, F., Gevers, W., De Moor, W., & Verguts, T. (2008). Dissecting the symbolic distance effect: Comparison and priming effects in numerical and nonnumerical orders. Psychonomic Bulletin & Review, 15(2), 419–425.CrossRefGoogle Scholar
  29. Vanbinst, K., Ghesquière, P., & De Smedt, B. (2014). Does numerical processing uniquely predict first graders’ future development of single-digit arithmetic? Learning and Individual Differences,. doi: 10.1016/j.lindif.2014.12.004.Google Scholar
  30. Verguts, T., & Fias, W. (2004). Representation of number in animals and humans: a neural model. Journal of Cognitive Neuroscience, 16(9), 1493–1504. doi: 10.1162/0898929042568497.CrossRefGoogle Scholar
  31. Wagner, J. B., & Johnson, S. C. (2011). An association between understanding cardinality and analog magnitude representations in preschoolers. Cognition, 119(1), 10–22.CrossRefGoogle Scholar
  32. Wiese, H. (2003). Iconic and non-iconic stages in number development: The role of language. Trends in Cognitive Sciences, 7(9), 385–390. doi: 10.1016/S1364-6613(03)00192-X.CrossRefGoogle Scholar
  33. Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24, 220–251.CrossRefGoogle Scholar
  34. Zhao, H., Chen, C., Zhang, H., Zhou, X., Mei, L., Chen, C., & Dong, Q. (2012). Is order the defining feature of magnitude representation? An ERP study on learning numerical magnitude and spatial order of artificial symbols. PLoS ONE, 7(11), e49565. doi: 10.1371/journal.pone.0049565.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2016

Authors and Affiliations

  1. 1.Attention, Brain and Cognitive Development Group, Department of Experimental PsychologyUniversity of OxfordOxfordUK

Personalised recommendations